Robots are being developed which comprise at least one leg link, which move by repeating movements to swing the leg link forward in the direction in which the robot attempts to move, and to make the leg link that has been swung forward and grounded become the support leg. It is known that legged robots like these can achieve a stable walking movement by controlling them based on the ZMP (Zero Moment Point). ZMP means the point on the floor at which the sum of the moments caused by external forces (including inertia) applied to the robot is equal to zero. Even in a state in which only one leg link is grounded, the robot will not fall if the ZMP is inside the foot plane of the support leg. For example, in the case of a robot that comprises two leg links, the robot will move by making one leg link the support leg, making the other leg link the idle leg, and swinging the idle leg link forward. If, during this one leg grounded state, the ZMP is inside the foot plane of the support leg, the robot will not fall. If, during the time in which the leg link that was the idle leg is grounded and both leg links are grounded, the ZMP shifts from inside the foot plane of the leg link that was the support leg up until that point to inside the foot plane of the leg link that was newly grounded, the robot will not fall, and it will be possible for the robot to swing the leg link that was the support leg up until that point forward. When the robot swings the leg link (which was the support leg up until that point) forward, the robot will not fall if the ZMP is inside the foot plane of the new support leg. By repeating the aforementioned movements, the robot will not fall and can continue to walk.
Humans perform a variety of movements in addition to walking. It is desirable for a robot to be able to run, jump, and hop while maintaining balance. All of these types of movements are comprised of an aerial phase (a phase in which the robot is floating in mid-air). Only gravity is applied to the robot in the aerial phase, and the ZMP cannot be defined. Technology is needed that will stabilize the robot before and after the aerial phase.
Technology is being developed in order to achieve movements of legged robots that include an aerial phase. For example, Japanese Laid-Open Patent Application Publication 2004-142095 discloses technology which calculates the center of gravity pathway in which the ZMP calculated with a ZMP equation (an equation which calculates the ZMP from the posture of the robot and the chronological changes therein) matches a target ZMP, for the ground phase (the phase in which the robot is grounded on the floor) before and after the aerial phase. This technology will divide the movement of the robot into a plurality of time intervals. For a phase in which one of the leg links is grounded and is the support leg (e.g. the grounded phase) in the divided time intervals, an analytic solution of the center of gravity pathway is prepared in advance. The analytic solution has been calculated based on the assumption that (1) the ZMP pathway has no acceleration, (2) the height of the center of gravity is fixed, and (3) the outer moment is fixed. The center of gravity pathway is then calculated by applying a coefficient of that analytic solution in real time. Note that the word “pathway” in the present specification refers to data that describes the changes in position over time.
In addition, Japanese Laid-Open Patent Application Publication 2004-167676 also discloses technology that calculates the center of gravity pathway in which the ZMP calculated with a ZMP equation matches a target ZMP. With this technology as well, an analytic solution of the center of gravity pathway is prepared in advance. The analytic solution has been derived based upon the assumption that (1) the ZMP pathway has no acceleration, (2) the height of the center of gravity is fixed, and (3) the outer moment is fixed. The parameters of that analytic solution are applied in real time. In addition, the aforementioned analytic solution will be adjusted near the boundary between the non-grounded state and the grounded state in order to maintain the continuity of the center of gravity pathway.